Since the solution of the system is any point (x, y) where the relation between x and y is given by the equation x - 3y = 4, that means the system has an infinite number of solutions, therefore the second equation of the system is a line paralell to the line of the first equation.
Calculating the slope of each equation, we have:
[tex]\begin{gathered} x-3y=4 \\ 3y=x-4 \\ y=\frac{x}{3}-\frac{4}{3}\to\text{slope}=\frac{1}{3} \\ \\ 2x+Qy=8 \\ Qy=-2x+8 \\ y=\frac{-2x}{Q}+\frac{8}{Q}\to slope=-\frac{2}{Q} \end{gathered}[/tex]Since the lines are paralell, they have the same slope, so:
[tex]\begin{gathered} \frac{1}{3}=-\frac{2}{Q} \\ Q=-2\cdot3 \\ Q=-6 \end{gathered}[/tex]